Modeling Star Distribution Using Spatial Poisson Process
(2025) In Bachelor’s Theses in Mathematical Sciences MASK11 20251Mathematical Statistics
- Abstract
- This thesis explores the Poisson process in one and multiple dimensions, with particular focus
on its application to modeling the spatial distribution of stars. The theory of both homogeneous
and inhomogeneous Poisson processes is developed, along with key aspects such as thinning,
distribution of inter-arrival times and nearest neighbor distribution. These are then extended
to a three-dimensional setting.
Two main applications of the Poisson process are considered, both modeling stars as inde-
pendent points in three-dimensional space. First, we study the probability that two stars are
mutually nearest neighbors, with the help of the nearest neighbor distribution and spatial ge-
ometry. Second, we estimate the expected number of... (More) - This thesis explores the Poisson process in one and multiple dimensions, with particular focus
on its application to modeling the spatial distribution of stars. The theory of both homogeneous
and inhomogeneous Poisson processes is developed, along with key aspects such as thinning,
distribution of inter-arrival times and nearest neighbor distribution. These are then extended
to a three-dimensional setting.
Two main applications of the Poisson process are considered, both modeling stars as inde-
pendent points in three-dimensional space. First, we study the probability that two stars are
mutually nearest neighbors, with the help of the nearest neighbor distribution and spatial ge-
ometry. Second, we estimate the expected number of stars visible to the naked eye, in order to
derive the probability distribution function of this number. This involves applying thinning,
as stars that are not bright enough to be seen should be excluded. We consider processes with
both homogeneous and inhomogeneous intensity. (Less) - Popular Abstract
- Have you ever wondered how many stars you can see in the night sky? Have you ever tried
to count them? Probably not - it would take ages. Unlike astronomical databases, statisti-
cians cannot give you the exact number, but they can o!er something else: the probability
distribution of the number of stars you might see.
Having that, we can answer many more questions. For example: How likely is it that you see a
certain number of stars? What is the expected number of visible stars? What is the expected
distance from the Sun to its nearest neighboring star? And how likely is it that the Sun is also
the nearest neighbor of that star?
To tackle these questions, we treat stars as randomly and independently located points in space
and... (More) - Have you ever wondered how many stars you can see in the night sky? Have you ever tried
to count them? Probably not - it would take ages. Unlike astronomical databases, statisti-
cians cannot give you the exact number, but they can o!er something else: the probability
distribution of the number of stars you might see.
Having that, we can answer many more questions. For example: How likely is it that you see a
certain number of stars? What is the expected number of visible stars? What is the expected
distance from the Sun to its nearest neighboring star? And how likely is it that the Sun is also
the nearest neighbor of that star?
To tackle these questions, we treat stars as randomly and independently located points in space
and apply a statistical model known as the Poisson process. This method is used for modeling
seemingly random sequences of events or points and despite its simplicity, provides a lot of
information about the events. Thorough theoretical treatment of the Poisson process and its
application to stars along with answering the aforementioned questions are the central topic
of this thesis. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9199459
- author
- Kostercová, Viktória LU
- supervisor
- organization
- course
- MASK11 20251
- year
- 2025
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor’s Theses in Mathematical Sciences
- report number
- LUNFMS-4080-2025
- ISSN
- 1654-6229
- other publication id
- 2025:K7
- language
- English
- id
- 9199459
- date added to LUP
- 2025-06-23 15:57:53
- date last changed
- 2025-06-23 15:57:53
@misc{9199459, abstract = {{This thesis explores the Poisson process in one and multiple dimensions, with particular focus on its application to modeling the spatial distribution of stars. The theory of both homogeneous and inhomogeneous Poisson processes is developed, along with key aspects such as thinning, distribution of inter-arrival times and nearest neighbor distribution. These are then extended to a three-dimensional setting. Two main applications of the Poisson process are considered, both modeling stars as inde- pendent points in three-dimensional space. First, we study the probability that two stars are mutually nearest neighbors, with the help of the nearest neighbor distribution and spatial ge- ometry. Second, we estimate the expected number of stars visible to the naked eye, in order to derive the probability distribution function of this number. This involves applying thinning, as stars that are not bright enough to be seen should be excluded. We consider processes with both homogeneous and inhomogeneous intensity.}}, author = {{Kostercová, Viktória}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor’s Theses in Mathematical Sciences}}, title = {{Modeling Star Distribution Using Spatial Poisson Process}}, year = {{2025}}, }